Dissecting a Regular Triangle into Three Similar Tiles

Dissecting a regular triangle into three similar polygons, two of them of the same size, looks quite impossible at first glance.

Hence it is no wonder that this problem was unsolved until 1987, when the author of this Demonstration stumbled upon it as part of working on his book A Puzzling Journey To The Reptiles And Related Animals on irregular rep-tiles. The surprising solution can also be found in his Zilllions game 'Isolattice'. The solution became widely known when Martin Gardner published it.